A general reduction theory for field theoretical Lagrangians on principal fiber bundles is presented. The reduced variational problem as well as the associated equations are formulated. The link between the solutions of the original problem and that of the reduced problem is discussed and an obstruction to the reconstruction of the solutions is isolated. The important case of semidirect products is discussed in detail and several concrete examples are presented.
A generalized symplectic structure on the bundle of connections p : C(P ) → M of an arbitrary principal G-bundle π : P → M is defined by means of a p * adP -valued differential 2-form Ω 2 on C(P ), which is related to the generalized contact structure on J 1 (P ). The Hamiltonian properties of Ω 2 are also analyzed. Classification (1991):53C05, 17B66, 22E65, 58A20, 58F05.
Mathematics Subject
In this article we introduce a novel method of making recommendations to groups based on existing techniques of collaborative filtering and taking into account the group personality composition. We have tested our method in the movie recommendation domain and we have experimentally evaluated its behavior under heterogeneous groups according to the group personality composition.
Abstract. Let π : P → M n be a principal G-bundle, and let L : J 1 P → Λ n (M ) be a G-invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian l defined on C(P ), the bundle of connections on P .
This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map JL are required apart from the momentum being a regular value of JL. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler-Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler-Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric. MSC2000: Primary 70H33. Secondary 70G65, 70H03, 53D20.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.